We propose to study different methods for constructing group sequential tests for the comparison of failure time distribution among different treatment groups using standard nonparametric tests for censored survival analysis. The operating characteristics and early stopping properties of these different group sequential tests will be investigated for different combination of patient entry rate, failure rates, and treatment difference alternatives. As a result of this research, guidelines will be provided for the efficient design of clinical trials that allow for early stopping. These sequential methods will also be extended to include adjustment for multiple covariates and time trend. We also propose to study the construction of confidence intervals for the hazard ratio under the assumption of a proportional hazards model following a group sequential test.